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Hi,I have a very urgent question on asymptotic distribution, and hope someone can give me some help.X_i is IID normal (0, sigma^2), i = 1,...,nX_bar = average of X_i'sS = average of the X_i^2'sthen the question is what is the asymptotic distribution of the X_bar/S?I know that X_bar is asymptotically normal with mean 0 and variance sigma^2and S is asymptotically normal with mean sigma^2 and variance 2*sigma^4. Thanks a lot!

is it just the asmptotic distribution of the X_bar/sigma^2?

The distribution of is a t with n degrees of freedom. When n goes to infinity, t goes to Normal.